Sehwag's 293, a robust 100 not out from skipper Mahendra Singh Dhoni and a string of half-centuries by the middle order fired the hosts to their highest ever total of 726-9 declared in reply to Sri Lanka's 393.
The tourists, trailing by 333 runs on the first innings, were 11-0 in their second knock at stumps on the third day on a wearing track at the Brabourne stadium.
Tharanga Paranavitana and Tillakaratne Dilshan survived three overs of spin before close, but Sri Lanka face a daunting task to avoid defeat over the next two days.
India's total surpassed their previous best of 705-7 declared against Australia at the Sydney cricket ground in January, 2004.
Sehwag had moved from his overnight score of 284 to 293 when he tapped a flighted ball from Muttiah Muralitharan back to the bowler who took the catch on second attempt.
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A hush descended at the stadium where some 15,000 home fans had packed the stands anticipating a world record by the swashbuckling opener.
Sehwa